Better I think would be to say "the result in column i and row j is the sum of product of elements in column i of the left cracovian and column j of the right cracovian".
And even by this definition the example given doesn't seem to track (and the strangeness of sometimes saying "+" and sometimes not, and having both "0" and "-0" in the example is bananas!):
{ 3 2 } { 1 -4 } = { 5 -2 }
{ -1 0 } { -2 3 } = { 0 2 }
3 * 1 + -1 * -2 == 5 -- check
3 * -4 + -1 * 3 == -15 -- what?
2 * 1 + 0 * -2 == 2 (okay, but shouldn't this be in the lower left, column 1 dotted with column 2?)
2 * -4 + 0 * 3 = -8 (now I'm really missing something)
Better I think would be to say "the result in column i and row j is the sum of product of elements in column i of the left cracovian and column j of the right cracovian".
And even by this definition the example given doesn't seem to track (and the strangeness of sometimes saying "+" and sometimes not, and having both "0" and "-0" in the example is bananas!):
{ 3 2 } { 1 -4 } = { 5 -2 }
{ -1 0 } { -2 3 } = { 0 2 }
3 * 1 + -1 * -2 == 5 -- check
3 * -4 + -1 * 3 == -15 -- what?
2 * 1 + 0 * -2 == 2 (okay, but shouldn't this be in the lower left, column 1 dotted with column 2?)
2 * -4 + 0 * 3 = -8 (now I'm really missing something)
Two things made it go viral.
1. Jason Kottke posted it to his weblog. Either you know about Kottke or you don't. Many journalists do. He's an authentic low-key tastemaker.
2. I shared the map on Flickr with a CC by-SA license. Which meant any publication could republish it for free without even asking me.
I'm still a little embarrassed about it. The map is pretty simple. The visualization is highly misleading and has all sorts of ugly visual artifacts. That Daily Mail article is full of mistakes (including misspelling my name three different ways.) The picture wasn't even really my goal, it was just a debugging workprint off my "real" project, a GitHub repo teaching people how to make maps in Javascript with vector tiles. But the picture looked cool and was easy to understand.
But I'm also proud of the result. It did look cool! And the recognition pleased my vanity. If I wanted I could have landed several years of consulting work off the momentary fame, I had all sorts of requests for custom work based on it. My favorite outcome was the artist Tamsie River took the data, made a giant mold, and poured a hot iron cast of the Mississippi watershed. I'm still sorry I didn't go for the event. https://tamsie.com/River%20of%20Iron.html
Late advice: when making a viral image, put your URL on it :-)
[1] https://marcinciura.wordpress.com/2015/09/17/smiths-millers-...
I was expecting Euclid's Elements to be up there. Perhaps the filter "literary work" disqualified it.
If you all pardon an off topic digression, the nebulosity of the definition of a straight line in elements has always bothered me. I wanted something free of reference to a physical artifact (straight edge, taught rope etc) and free of algebra. Its sometimes defined in terms of reflections or rotations or translations, but then that begs the question what is a straight axis (or direction of translation). Playfair's version is almost satisfactory. The standard I guess is Hilbert's.
IMHO, Euclid's definition of a straight line in today's terms would be "a line that has the same direction on its entire length". His definition of a plane angle would be "a plane angle is the difference between the directions of two straight lines that have a common end in one point".
What are Playfair's and Hilbert's definitions?
A unit quaternion represents a rotation in R³.
A quaternion represents the quotient of two vectors in R³. That's what Hamilton had in mind.